This proposal reflects our continuing interest in the development of new statistical methods, and their application to problems related to diet, physical activity and cancer. The projects mentioned here will be undertaken with NCI scientists specializing in nutrition, physical activity and statistics. The P.I. has visited the NCI on many occasions, including 3 sabbaticals, the most recent being in 2013-2014. An important outgrowth of these continuing relationships is that we have access to a large number of unique data sets, the analysis of which will guide our research program. Locally, besides the P.I., we have assembled a team that has experts in a wide variety of statistical methodology relevant to diet, physical activity and cancer outcomes. In specific aim 1 we will develop new models and methods for the analysis of dietary patterns, a field of major importance in nutrition. This will include analyzing many dietary components simultaneously, estimating from short term instruments the number of people who do not consume certain dietary components, e.g., alcoholic beverages, and building new dietary indices that combine adherence to dietary guidelines with power to predict the risk of cancer and other health outcomes. In specific aim 2, we explain that the assessment of dietary intakes and physical activity is being revolutionized by new technologies, including web-based instruments, increasing use of accelerometers, longer-term studies with repeated dietary assessment, and biomarker studies. To take advantage of these new data structures, we will propose a series of projects including physical activity pattern analysis and risk, within and between individual variance function esti- mation, modeling of time-varying usual dietary intake and physical activity with interactions, and misclassification and measurement error, and latent variable models. In specific aim 3, we will develop new methods for the analysis of case-control studies, including the analysis of gene-environment interactions on risk, efficient semi parametric regression in the analysis of secondary outcomes.